单层球面网壳结构找形研究

Form-finding of single-layer reticulated domes

将柔性结构中找形的概念应用于刚性结构,提出基于力密度法的球面网壳结构的找形方法.在找形过程中考虑自重,解决了高斯曲率为正的球面网壳的找形问题,并且通过找形基本消除了自重引起的弯矩和剪力.找形得到的网壳结构与传统的球面网壳在曲面外形上仅有微小的差别,但网格划分更均匀,几何形体更优美,承载能力也有较大幅度的提高.本文提出的找形方法收敛性好,效率高,为球面网壳结构的设计提供了新的方法和思路.

By applying the concept of form-finding used in flexible structures into rigid structures, this paper presents a form-finding method for single-layer reticulated domes based on the force density method. The form-finding of reticulated domes with positive Gaussian curvature is realized by introducing the selfweight of the structure into the form-finding process, and the bending moments and shear forces caused by the self-weight could be minimized through the process. The geometrical shape of form-finding latticed shell is close to that of the traditional reticulated domes, but with more even grid mesh and more elegant shape and will enbance the stability bearing capacity of the structure. The proposed form-finding method is of good convergence and high efficiency, providing a new approach for the design of reticulated domes.